Statistics Descriptive Statistics | Study Guide

University:
Bradley University
Course:
MTH 325 | Probability and Statistics I
Academic year:

2022
Views:

344

Pages:

2
Author:

Marin Mason

DESCRIPTIVE STATISTICS FREQUENCY DISTRIBUTIONS A representation, either in a graphical or tabular format, that displays the number of observations within a given interval. The intervals must be mutually exclusive and exhaustive. An example of frequency distributions: Height Frequency 67in 3 62in 1 64in 5 70in 2 GRAPH OF FREQUENCY DISTRIBUTION MEASURES OF CENTER The four measures of center are mean, median, mode, and midrange. ● Mean - The average ● Median - Measure of center ● Mode - The value that appears most often. ● Midrange - The midway between the least and greatest value of the set. WEIGHTED MEANS A kind of average that instead of each data point contributing equally to the final mean, some data points contribute more “weight” than others. MEASURES OF VARIATIONS Summary measures to describe the amount of variability or spread in a set of data. The most common measures of variability are the range, the interquartile range (IQR), variance, and standard deviation. ● Standard deviation: A statistic that measures the dispersion of a dataset in relation to its mean and is calculated as the square root of the variance. ○ Example - The mean of the following two is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30. However, the second is more spread out. If a set has a low standard deviation, the values are not as spread out. ● IQR: The middle 50% of values when ordered from lowest to highest. ○ To find the interquartile range (IQR), first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1. ○ Example - Consider the following numbers: 1, 3, 4, 5, 5, 6, 7, 11. Q1 is the middle value in the first half of the data set. ... The interquartile range is Q3 minus Q1, so IQR = 6.5 - 3.5 = 3. ● Range: The difference between the lowest and highest values. ○ Example - In (4, 6, 9, 3, 7) the lowest value is 3, and the highest is 9, so the range is 9 − 3 = 6.